Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Table of contents

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[101.] PROP. XXXI. PROBLEMA. Ex dato arcu invenire ſinum.
[102.] PROP. XXXII. PROBLEMA. Invenire quadratum æquale ſpatio hyperbolico con-tento à curva hyperbolica, uno aſymptoto & dua-bus rectis alteri aſymptoto parallelis; quod ſpatium æquale eſt ſectori hyperbolico cujus baſis eſt eadem curva.
[103.] PROP. XXXIII. PROBLEMA. Propoſiti cujuscunque numeri logorithmum invenire.
[104.] SCHOLIUM.
[105.] PROP. XXXIV. PROBLEMA. Ex dato logorithmo invenire ejus numerum.
[106.] Tom. II. Mmm
[107.] PROP. XXXV. PROBLEMA. Rectâ per datum punctum in diametro ductâ, ſemicirculum in ratione data dividere.
[108.] SCHOLIUM.
[109.] FINIS.
[110.] II. HUGENII OBSERVATIONES IN LIBRUM JACOBI GREGORII, DE VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
[111.] III. DOMINI GREGORII RESPONSUM AD ANIMADVERSIONES DOMINI HUGENII, IN EJUS LIBRUM, DE VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
[112.] PROP. X. PROBLEMA.
[113.] Tom. II. Nnn
[114.] CONSECTARIUM.
[115.] IV. EXCERPTA EX LITERIS Dni. HUGENII DE RESPONSO, QUOD Dnus. GREGORIUS DEDIT AD EXAMEN LIBRI, CUI TITULUS EST, VERA CIRCULI ET HYPERBOLÆ QUADRATURA.
[116.] V. EXCERPTA EX EPISTOLA D. JACOBI GREGORII, CONTINENTE QUASDAM EJUS CONSIDERATIO-NES, SUPER EPISTOLA D. HUGENII, IMPRESSA IN VINDICATIONEM EXAMINIS SUI LIBRI, DE VERA CIRCULI ET HY-PERBOLÆ QUADRATURA.
[117.] FINIS.
[118.] CHRISTIANI HUGENII GEOMETRICA VARIA. Tom. II. Ppp
[119.] I. CONSTRUCTIO LOCI AD HYPERBOLAM PER ASYMPTOTOS.
[120.] DEMONSTRATIO.
[121.] II. DEMONSTRATIO REGULÆ DE MAXIMIS ET MINIMIS.
[122.] Tom. II. Qqq
[123.] III. REGULA Ad inveniendas Tangentes linearum curvarum.
[124.] Tom. II. Rrr
[125.] IV. CHRISTIANI HUGENII EPISTOLA DE CURVIS QUIBUSDAM PECULIARIBUS.
[126.] V. PROBLEMA AB ERUDITIS SOLVENDUM: A JOHANNE BERNOULLIO IN ACTIS LIPSIENSIBUS ANNI MDCXCIII. PROPOSITUM.
[127.] Tom. II. Ttt
[128.] VI. C. H. Z. DE PROBLEMATE BERNOULLIANO IN ACTIS LIPSIENSIBUS PROPOSITO.
[129.] VII. C. H. Z. CONSTRUCTIO UNIVERSALIS PROBLEMATIS A CLARISSIMO VIRO JOH. BERNOULLIO PROPOSITI.
[130.] FINIS.
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            <s xml:id="echoid-s4413" xml:space="preserve">
              <pb o="480" file="0200" n="210" rhead="JAC. GREG. CONSID."/>
            cujus poteſtatis puræ, ſive affectæ ad puram irreducibilis.
              <lb/>
            </s>
            <s xml:id="echoid-s4414" xml:space="preserve">Nam ſi Sector eodem modo fiat cx primis terminis conver-
              <lb/>
            gentibus, quo ex ſecundis (ut in Conſect. </s>
            <s xml:id="echoid-s4415" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s4416" xml:space="preserve">10. </s>
            <s xml:id="echoid-s4417" xml:space="preserve">eſt de-
              <lb/>
            monſtratum) etiam omnes ejus poteſtates ſive puræ, ſive
              <lb/>
            quocunque modo affectæ eodem modo componitur è pri-
              <lb/>
            mis, quo è ſecundis terminis convergentibus, quæ (in A-
              <lb/>
            nalyticis exhibitæ) erunt æquales quantitates eodem modo
              <lb/>
            Analyticè compoſitæ ex primis, quo ex ſecundis terminis
              <lb/>
            convergentibus; </s>
            <s xml:id="echoid-s4418" xml:space="preserve">quod eſt abſurdum, nempe contra Prop. </s>
            <s xml:id="echoid-s4419" xml:space="preserve">
              <lb/>
            11. </s>
            <s xml:id="echoid-s4420" xml:space="preserve">admiſlam. </s>
            <s xml:id="echoid-s4421" xml:space="preserve">Senſus igitur integer Prop. </s>
            <s xml:id="echoid-s4422" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4423" xml:space="preserve">eſt Hoc Pro-
              <lb/>
            blema (E datis duobus polygonis complicatis, invenire Se-
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            ctorem ſive Circularem ſive Hyperbolicum ab illis determi-
              <lb/>
            natum) non poteſt reduci ad ullam æquationem Analyticam.</s>
            <s xml:id="echoid-s4424" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4425" xml:space="preserve">In comparatione Hugeniana inter noſtras methodos, a-
              <lb/>
            gnoſco, meas approximationes prop. </s>
            <s xml:id="echoid-s4426" xml:space="preserve">20. </s>
            <s xml:id="echoid-s4427" xml:space="preserve">& </s>
            <s xml:id="echoid-s4428" xml:space="preserve">21. </s>
            <s xml:id="echoid-s4429" xml:space="preserve">eaſdem eſſe
              <lb/>
            cum Hugenianis, ſed methodo mihi peculiari demonſtratas.
              <lb/>
            </s>
            <s xml:id="echoid-s4430" xml:space="preserve">At meam approximationem in fine prop. </s>
            <s xml:id="echoid-s4431" xml:space="preserve">25. </s>
            <s xml:id="echoid-s4432" xml:space="preserve">non percipere
              <lb/>
            videtur Hugenius; </s>
            <s xml:id="echoid-s4433" xml:space="preserve">aliam interim ſibi fingit: </s>
            <s xml:id="echoid-s4434" xml:space="preserve">hanc primò
              <lb/>
            meam non eſſe probat, deinde tamen eam cum ſua compa-
              <lb/>
            rat, victoriaque potitur. </s>
            <s xml:id="echoid-s4435" xml:space="preserve">Sed lentè hic feſtinandum.</s>
            <s xml:id="echoid-s4436" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4437" xml:space="preserve">Sit a Polygonum, Circulo vel ſectori inſcriptum, c Po-
              <lb/>
            lygonum inſcriptum duplo plura habens latera, d autem ſit
              <lb/>
            Polygonum circumſcriptum ſimile ipſi c. </s>
            <s xml:id="echoid-s4438" xml:space="preserve">Ex 20. </s>
            <s xml:id="echoid-s4439" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s4440" xml:space="preserve">Sector
              <lb/>
            eſt major quam {4c - a;</s>
            <s xml:id="echoid-s4441" xml:space="preserve">/3} & </s>
            <s xml:id="echoid-s4442" xml:space="preserve">ex 21. </s>
            <s xml:id="echoid-s4443" xml:space="preserve">Sector eſt minor quam
              <lb/>
            {2d + c/3}, inter quos terminos ſit maximus quatuor continuè
              <lb/>
            proportionalium {8d + 8c-a/15}, nempe noſtra approximatio@
              <lb/>
            quam rigidiſſimis Hugenii cenſuris ſubjicio. </s>
            <s xml:id="echoid-s4444" xml:space="preserve">Hallucinatur au-
              <lb/>
            tem Hugenius, quod Polygona a & </s>
            <s xml:id="echoid-s4445" xml:space="preserve">d ſimilia ſumeret, cum
              <lb/>
            debeant eſſe c & </s>
            <s xml:id="echoid-s4446" xml:space="preserve">d, quæ duplò plura habent latera. </s>
            <s xml:id="echoid-s4447" xml:space="preserve">Ne
              <lb/>
            autem dicat, factam eſſe à me correctionem, conſideret
              <lb/>
            hanc approximationem non ſolum verbis prop. </s>
            <s xml:id="echoid-s4448" xml:space="preserve">25. </s>
            <s xml:id="echoid-s4449" xml:space="preserve">ſed & </s>
            <s xml:id="echoid-s4450" xml:space="preserve">
              <lb/>
            praxi prop. </s>
            <s xml:id="echoid-s4451" xml:space="preserve">30. </s>
            <s xml:id="echoid-s4452" xml:space="preserve">eſſe conſonam, ubi approximationem prop.
              <lb/>
            </s>
            <s xml:id="echoid-s4453" xml:space="preserve">21. </s>
            <s xml:id="echoid-s4454" xml:space="preserve">ex ultimis ſimilibus Polygonis conſtruo: </s>
            <s xml:id="echoid-s4455" xml:space="preserve">ridiculum enim
              <lb/>
            eſſet, illam è penultimis minus præciſam dare, cum </s>
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